From a Bayesian perspective the natural solution is to form an (approximate) posterior over the weights of the neural networks. To investigate, we consider a state-of-the-art implementation of a post-hoc Laplace approximation [1]} of the weight posterior. This amounts to training a regular autoencoder, and thereafter approximating the weight uncertainty with the Hessian of the loss (Sec. REF ). fig:teaserb shows that uncertainty now grows, as intuitively expected, with the distance to the data distribution, but there seems to be little semantic structure in the uncertainty in output space. This suggests that while the post-hoc procedure is computationally attractive it is too simplistic. 
